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One does not simply predict where the other will go, which is wherever the first predicts the second to predict the first to go, and so ad infinitum. Not "What would I do if I were she?" but "What would I do if I were she wondering what she would do if she were wondering what I would do if I were she...?".
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A Treatise of Human Nature (1739-40).David Hume - 1978 - Oxford University Press.
Theory of Games and Economic Behavior.John Von Neumann & Oskar Morgenstern - 1944 - Princeton, NJ, USA: Princeton University Press.
Convention: A Philosophical Study.David Lewis - 1969 - Synthese 26 (1):153-157.
The Stability Theory of Belief.Hannes Leitgeb - 2014 - Philosophical Review 123 (2):131-171.

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